### Abstract

Gaseous fuel is injected at a constant rate M from the bottom of a narrow insulated chamber and oxidant diffuses from the top. The object is to determine the response curve, i.e. the unburnt fuel fraction R as a function of M for fixed Damköhler number (representing either the constant chamber pressure or the chamber's length). The conclusions we draw are based on activation-energy asymptotics. Explicit response curves are obtained over the whole range of D. Two critical values D_{a}, D_{0} are uncovered and determined explicitly. If D < D_{a} the fuel will not burn: R ≡ 1 (extinguished state). If D_{a} < D < D_{0} a closed curve, called an isola, is also a possible response; its base lies on R = 0 (complete burning) and its upper part corresponds to a partial burning of fuel. If D > D_{0} the response is S-shaped: the top of the curve lies on R = 1 and extends to M → ∞; the bottom lies on R = 0 and persists however small M becomes. The isola has two extinction points, corresponding to the fuel being supplied too slowly or too fast to a flame at the bottom or top of the chamber. The S has just the latter, but also has an ignition point; as M is decreased through the corresponding value the flame suddenly appears. The asymptotic analysis completes the inadequate picture obtained previously by numerical methods. It spans the whole range of parameter values and enables explicit formulas to be written for the ignition and extinction points.

Original language | English (US) |
---|---|

Pages (from-to) | 943-959 |

Number of pages | 17 |

Journal | Acta Astronautica |

Volume | 6 |

Issue number | 7-8 |

DOIs | |

State | Published - Jan 1 1979 |

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### ASJC Scopus subject areas

- Aerospace Engineering

### Cite this

*Acta Astronautica*,

*6*(7-8), 943-959. https://doi.org/10.1016/0094-5765(79)90080-8

**Diffusion flames in a chamber.** / Matalon, M.; Ludford, G. S.S.; Buckmaster, J.

Research output: Contribution to journal › Article

*Acta Astronautica*, vol. 6, no. 7-8, pp. 943-959. https://doi.org/10.1016/0094-5765(79)90080-8

}

TY - JOUR

T1 - Diffusion flames in a chamber

AU - Matalon, M.

AU - Ludford, G. S.S.

AU - Buckmaster, J.

PY - 1979/1/1

Y1 - 1979/1/1

N2 - Gaseous fuel is injected at a constant rate M from the bottom of a narrow insulated chamber and oxidant diffuses from the top. The object is to determine the response curve, i.e. the unburnt fuel fraction R as a function of M for fixed Damköhler number (representing either the constant chamber pressure or the chamber's length). The conclusions we draw are based on activation-energy asymptotics. Explicit response curves are obtained over the whole range of D. Two critical values Da, D0 are uncovered and determined explicitly. If D < Da the fuel will not burn: R ≡ 1 (extinguished state). If Da < D < D0 a closed curve, called an isola, is also a possible response; its base lies on R = 0 (complete burning) and its upper part corresponds to a partial burning of fuel. If D > D0 the response is S-shaped: the top of the curve lies on R = 1 and extends to M → ∞; the bottom lies on R = 0 and persists however small M becomes. The isola has two extinction points, corresponding to the fuel being supplied too slowly or too fast to a flame at the bottom or top of the chamber. The S has just the latter, but also has an ignition point; as M is decreased through the corresponding value the flame suddenly appears. The asymptotic analysis completes the inadequate picture obtained previously by numerical methods. It spans the whole range of parameter values and enables explicit formulas to be written for the ignition and extinction points.

AB - Gaseous fuel is injected at a constant rate M from the bottom of a narrow insulated chamber and oxidant diffuses from the top. The object is to determine the response curve, i.e. the unburnt fuel fraction R as a function of M for fixed Damköhler number (representing either the constant chamber pressure or the chamber's length). The conclusions we draw are based on activation-energy asymptotics. Explicit response curves are obtained over the whole range of D. Two critical values Da, D0 are uncovered and determined explicitly. If D < Da the fuel will not burn: R ≡ 1 (extinguished state). If Da < D < D0 a closed curve, called an isola, is also a possible response; its base lies on R = 0 (complete burning) and its upper part corresponds to a partial burning of fuel. If D > D0 the response is S-shaped: the top of the curve lies on R = 1 and extends to M → ∞; the bottom lies on R = 0 and persists however small M becomes. The isola has two extinction points, corresponding to the fuel being supplied too slowly or too fast to a flame at the bottom or top of the chamber. The S has just the latter, but also has an ignition point; as M is decreased through the corresponding value the flame suddenly appears. The asymptotic analysis completes the inadequate picture obtained previously by numerical methods. It spans the whole range of parameter values and enables explicit formulas to be written for the ignition and extinction points.

UR - http://www.scopus.com/inward/record.url?scp=0018491607&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0018491607&partnerID=8YFLogxK

U2 - 10.1016/0094-5765(79)90080-8

DO - 10.1016/0094-5765(79)90080-8

M3 - Article

AN - SCOPUS:0018491607

VL - 6

SP - 943

EP - 959

JO - Acta Astronautica

JF - Acta Astronautica

SN - 0094-5765

IS - 7-8

ER -